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O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2018 · Q128 Marks

A curve is such that d²y/dx² = (2x - 5)⁻^(1/2). Given that the curve has a gradient of 6 at the point (9/2, 2/3), find the equation of the curve.

  1. A curve is such that d²y/dx² = (2x - 5)⁻^(1/2). Given that the curve has a gradient of 6 at the point (9/2, 2/3), find the equation of the curve.[8]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

  1. [M1] for k(2x-5)^(1/2)
  2. [A1] for (2x-5)^(1/2)
  3. [M1dep] Substitution to obtain arbitrary constant
  4. [A1] for correct dy/dx
  5. [M1dep] on first M1 for integration of k(2x-5)^(1/2) to obtain m(2x-5)^(3/2)
  6. [A1] for (1/3)(2x-5)^(3/2) + 4x (FT their (non -zero) constant)
  7. [M1dep] for obtaining arbitrary constant
  8. [A1] for correct equation

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2018 Paper 1 Variant 1, question 12.

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